Question

In ΔRST, if m∠R is five times more than twice x, m∠S is one more than x, and m∠T is sixteen less than seven times x, find x and the measure of each angle.

Answer 1

To find x and the measure of each angle in the triangle, use the given equations to set up an equation based on the sum of angles in a triangle. Solve the equation to find x and then calculate the measure of each angle using the given relationships.

To find x and the measure of each angle in the triangle, we need to use the given information about the angles and their relationships. Let's start with the given equations:

• m∠R = 5(2x)
• m∠S = x + 1
• m∠T = 7x - 16

From the first equation, we can simplify to: m∠R = 10x. From the second equation, we have: m∠S = x + 1. And from the third equation, we have: m∠T = 7x - 16.

Since the sum of angles in a triangle is always 180 degrees, we can write the equation: m∠R + m∠S + m∠T = 180. Substituting the given equations into this equation, we get (10x) + (x + 1) + (7x - 16) = 180. Solving this equation will help us find x and then we can find the measure of each angle.

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